Extrapolating POD reduced-order model based on temperature gradient for unsteady heat conduction

Abstract

A new proper orthogonal decomposition (POD) reduced-order model based on temperature gradient is established for heat conduction differential equation. In the most of present studies of heat conduction POD reduced-order model, the POD basis functions are extracted from temperature fields by adopting proper orthogonal decomposition or singular value decomposition (SVD). Different from conventional POD reduced-order method, this paper optimize the gradient of POD solutions by extracting the optimal orthogonal basis from temperature gradient. After getting POD basis, the POD reduced-order model is solved by using Galerkin projection. POD-Galerkin reduced-order model of two dimensional, constant property and non-steady heat conduction differential equations is established, and the accuracy of the reduced-order model under different boundary conditions is further studied. The results suggests that the relative error of POD solution is less than 0.1% while the average computing time reduces from 1.64 s to 0.02 s.